16.362 signal and system i system function algebra and block diagram representation + + -
TRANSCRIPT
16.362 Signal and System I System function algebra and block diagram representation
)()(1
)()(
21
1
zHzH
zHzH
+][nx )(1 zH
)(2 zH
)()()()()( 21 zHzYzXzHzY
+
-][ny
16.362 Signal and System I System function algebra and block diagram representation
1
41
1
1)(
zzH
+][nx
1z
][ny
][]1[4
1][ nxnyny
4
1
16.362 Signal and System I
1
1
41
1
21)(
z
zzH
+][nx
1z
][ny
]1[2][]1[4
1][ nxnxnyny
4
1
+
2
16.362 Signal and System I
21
21
81
41
1
21
47
1)(
zz
zzzH
+][nx
1z
][ny
4
1
+
4
7
1z
8
1
+
2
1
+
16.362 Signal and System I The unilateral z-transform
0
][)(n
nznxzX
Example ][]1[3][ nxnyny ][][ naunx ?][ ny
Bilateral z-transform
131
1)(
zzH
11)(
z
azX
11 131)(
zz
azY
11 1
4/
31
4/3)(
z
a
z
azY
][4
][34
3][ nu
anu
any n ]0[]0[ xy 0]1[ y
16.362 Signal and System I The unilateral z-transform
0
][)(n
nznxzX
Shift property
]1[)(]1[)( 1
1
11
xzzznxzzn
n XX'
][nx
n
nznxzX ][)(
]1[ nx )(]1[)(' 111 zXzznxzzXn
n
The unilateral z-transform
][nx
]1[ nx
0
][)(n
nznxzX
]1[)()( 1 xzzz XX'
16.362 Signal and System I The unilateral z-transform
0
][)(n
nznxzX
Shift property
]0[)(]1[)(0
1 zxzzznxzzn
n
XX'
][nx
n
nznxzX ][)(
]1[ nx )(]1[)(' 1 zzXznxzzXn
n
The unilateral z-transform
][nx
]1[ nx
0
][)(n
nznxzX
]0[)()( zxzzz XX'
16.362 Signal and System I Example
Example ][]1[3][ nxnyny ][][ naunx ?][ ny
The unilateral z-transform
]1[y
)(]1[3)(3)( 1 zyzzz XYY
111 31
3
)1(31)(
zzz
az
Y
111 31
3
)1(
4/
31
4/3)(
zz
a
z
az
Y
]1[3]0[]0[ yxy
16.362 Signal and System I Example
Example ][]1[3][ nxnyny ][][ naunx ?][ ny
The unilateral z-transform
]1[y
a=8, =1
)1(
2
31
3)(
11
zzzY ][2][)3(3][ nununy n
111 31
3
)1(
4/
31
4/3)(
zz
a
z
az
Y
5]1[3]0[]0[ yxy